理想解相似度順序偏好法(Technique for Order Preference by Similarity to Ideal Solution; TOPSIS)是一項多屬性決策方法，藉由衡量方案於屬性之明確評估值與理想解的距離，對可行方案排序。在決策的過程中，決策者會因不同評選屬性的特性而選擇適當的方式進行評估，可採用的方式有明確數值、區間值或模糊語意，為了處理具模糊性的決策資訊，在模糊數運算過程中，必須進行解模糊化，因而導致決策資訊流失，使決策較不精確。因此，本研究以二元模糊語意表示法取代傳統語意變數，其運算能完整保留決策資訊。在決策過程中，評估屬性之權重亦是影響決策之關鍵因素，若僅由決策者直接決定評估屬性的權重過於主觀；此外，複雜的決策問題影響層面廣泛，單一決策者的知識與經驗背景會侷限思考的角度，有失公正客觀。
針對上述問題，本研究建構一模糊群體TOPSIS決策模式，決策流程主要可分為三個步驟，第一步驟將異質的評估資訊轉換為一致的二元模糊語意表示法，第二步驟同時考慮決策者的主觀意見及客觀的評估資訊，以二階段數學規劃法求得明確數值之評估屬性權重，最後將上述兩個步驟取得的數值代入修正之群體TOPSIS決策流程中運算，對可行方案排序，以評選出最佳方案。本研究以案例說明求解步驟，再與Halouani et al. (2009)所提出之模式進行比較與分析，驗證本決策模式之優勢。

關鍵字：二元模糊語意表示法、TOPSIS、多屬性決策、群體決策

The approach of “technique for order preference by similarity to ideal solution (TOPSIS)” is usually considered as a multi-attribute decision-making (MADM) method. It can determine the ranking for all the alternatives based on the measurement of the distance between crisp data and ideal solution. In decision-making processes, decision-makers choose the appropriate domain to assess alternatives due to the nature of the attributes. This non-homogeneous information can be represented as values belonging to domains with different nature as numerical, interval valued or linguistic. In order to deal with ambiguity existing in decision-making information, the defuzzification method is adopted in the operations of fuzzy numbers; however, the loss of decision-making information may happen. The loss of information implies a lack of precision in the decision results. This motivates the proposed method to apply the 2-tuple fuzzy linguistic representation to replace the traditional linguistic variables. Moreover, the attributes’ weights are also key factors which affect decision results. The direct determination of each attribute’s weight by decision makers could be too subjective for a decision-making problem. In addition, when many aspects affect complex decision problems, relying on only one decision maker’s knowledge and experience could produce an unreliable consequence.
To address these problems, we construct a TOPSIS group decision-making model which includes three stages. In the first stage, we transform the non-homogeneous information into the 2-tuple fuzzy linguistic representation. The second stage applies a two-step mathematical programming method which takes both decision maker's subjective opinion and objective information into account to determine attributes’ weights. Then we can rank all alternatives by the modified TOPSIS group decision-making model. Finally, a numerical example is performed using the proposed model to demonstrate its superiority, compared to Halouani et al. (2009).

Key words: 2-tuple fuzzy linguistic representation; TOPSIS; MADM; group decision-making

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